二维调和方程的概率数值解法

A Probabilistic Numerical Solution for the 2 - D Harmonic Equation

利用二维布朗运动与调和方程之间的联系,以及布朗运动一些特有的性质和圆上的泊松积分公式,给出了调和方程的一个概率数值解法。具体构造了圆周和较一般闭曲线上的剖分以及相应的函数,给出了理论上的分析和数值解的全过程。

By using the connections between a 2 - D Brown Motion and the harmonic equation, some of the properties for Brown Motion and Poisson integral formula we provide a probabilistic numerical solution for the harmonic e-quation. We also pratically construct the subdivision and functions over a circle and an ordinary closed curve. Both the theoretical analysis and the process of the method are shown.